What influence did Greek philosophy have on the formation of orthodox Christian doctrine?
Particularly, what Christian doctrines or paradigms of understanding God and reality can be traced to have been influenced by Greek thought?
There were a lot of things that Greeks taught and believed that resemble what mainstream Christianity has come to embrace. For example
The concept of a soul within us that cannot die first became a ‘Christian’ doctrine at the end of the second century AD. Hell had been taught in Greek philosophy long before the time of Jesus, with Plato (427-347 BC) as the important leader in this thinking. The teaching of an everlasting place of punishment for the wicked is the natural consequence of a belief in an immortal soul. By the year AD 187, it was understood that life, once we have it, is compulsory; there is no end to it, either now or in a world to come. We have no choice as to its continuance, even if we were to commit suicide to end it.
More detail given at Truth According to Scripture
The early church fathers though maybe influenced were very much sympathetic to many stoic philosphers ideas of morality being an abstract thing not to do with the gods. As a concept of morality being written on the heart, the early church fathers knew the motivation for the ideas of logos was because the roman and greek pantheon of gods did many immoral things so the romans had to get their heads around a deity that did good and was the source of good.
In 2018 I wrote an article titled "Ousía and hypostasis from the philosophers to the councils" which probably answers most of this question, so I will just link to it. It is also in PDF format in academia.edu.